Question: Solve for $x$ and $y$ using substitution. ${-3x-4y = 1}$ ${x = -5y+7}$
Solution: Since $x$ has already been solved for, substitute $-5y+7$ for $x$ in the first equation. ${-3}{(-5y+7)}{- 4y = 1}$ Simplify and solve for $y$ $15y-21 - 4y = 1$ $11y-21 = 1$ $11y-21{+21} = 1{+21}$ $11y = 22$ $\dfrac{11y}{{11}} = \dfrac{22}{{11}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x = -5y+7}\thinspace$ to find $x$ ${x = -5}{(2)}{ + 7}$ $x = -10 + 7$ ${x = -3}$ You can also plug ${y = 2}$ into $\thinspace {-3x-4y = 1}\thinspace$ and get the same answer for $x$ : ${-3x - 4}{(2)}{= 1}$ ${x = -3}$